Black Friday Post

Table of Contents

1. Introduction

2. What If? COVID-86

3. What If? COVID-91

4. What If? COVID-93

5. What If? COVID-96 (NEW)

6. What If? COVID-08

7. What If? COVID-14

8. Plans for Ethnostats

9. Cheng's Art of Logic in an Illogical World, Chapter 2

10. Conclusion

Introduction

Today is Black Friday, the day after Thanksgiving. It is, of course, a day strongly associated with shopping and sales. For the blog, it's a day to catch up with some topics that I don't have time to discuss when school is in session.

On my old blog, I established something I called "COVID What-Ifs." These are stories in which I seek to answer the question, "What if the COVID-19 pandemic had occurred when I was much younger?" I consider myself fortunate not to have had a pandemic during my youth, but my current students, of course, aren't so lucky.

I can never truly know what it's like to suffer through a pandemic as a child or teenager. But I can start to empathize with my students by placing the pandemic a different points in my life via these What Ifs.

I began these stories on the old blog, detailing how I would have felt at the time the schools closed. I continue the stories by discussing the reopening of the schools.

What If? COVID-86

The first What If? story is called "COVID-86." Just as the number 19 in "COVID-19" refers to the year 2019, the number 86 here refers to the year 1986. But notice that 19 refers to the date the coronavirus was first identified and reported in China -- December 31st, 2019. In other words, 2019 was a relatively normal year -- the first year when anyone outside of China was affected by the pandemic was 2020. So in the COVID-86 universe, 1986 is a normal year. Then 1987 is the year when the schools close.

In March 1987, I was a kindergartner -- and for these stories, I'm assuming that the schools close in March, just as they did in 2020 in the original timeline (that is, the real universe in which the disease is COVID-19, not COVID-86). So in this universe, I have most of a normal kindergarten year, then the schools are closed until late in my first grade year.

During the twelve months when the schools are closed, I participate in "distance learning" -- but here the definition of distance learning must match the technology of the year in which the What If? is set. I can't have any sort of Internet learning since that would be impossible in 1987-88. Instead, the distance learning consists of weekly packets of work which are picked up and dropped off at the school.

For the most part, I should have a normal second grade year under COVID-86. It will be nice to see my friends again, and my hope will be that I can have a regular year -- my first full school year.

In the original timeline, I call my second grade teacher my favorite teacher -- mainly because she borrowed a Pre-Algebra text from the middle school and allowed me to study independently. I'm not sure she'd still be able to do so if it's just during a pandemic -- everyone might be thinking too much about getting things back to normal and less about extras like Pre-Algebra for a young second grader.

What If? COVID-91

This is a totally separate universe. Here I place the pandemic when I'm a little older. Under COVID-91, the schools close in March 1992 when I'm a fifth grader, and they reopen a year later, during my sixth grade year (the last year at my K-6 elementary school).

In the n+2 year (in other words, 1993 in the COVID-91 universe, just like 2021 in the real COVID-19 universe), I enter my seventh grade year. This is the first year at my 7-12 high school.

I've followed how my old school is handling distance learning and the return to in-person. One thing I notice is that the school has switched to a completely different bell schedule. For these What If? stories, the rule of thumb is that if my old school makes any significant changes as a result of the pandemic, then those changes must propagate to the corresponding year in the What If? universe. This means that under COVID-91, my school must adopt this new schedule.

The old pre-pandemic schedule was a traditional six-period day. The new schedule is a block schedule, with all classes on Mondays, odd periods Tuesdays and Thursdays, and even periods the other days, a bit like the block schedule at the school where I currently teach.

Last week, I blogged about block schedules. In comparing the schedules at my current school and the main flagship high school, I pointed out that different schools have different ways to avoid having blocks last two hours -- introducing an Advisory period, having four blocks instead of three blocks, and so on.

The school I attended as a seventh grader is unusual in that it does two of these hacks. It has a one-hour Tutorial period at the end of the day, and each of the three class blocks ends with twenty minutes of "Embedded Support" (like one of the districts where I subbed last year). Thus the resulting periods (after deducting for embedded and tutorial) are slightly over 80 minutes in length. Also, school in 2021 starts half an hour later than it did before the pandemic (and 45 minutes later than it did back when I was a young seventh grader in 1993).

So in the COVID-91 universe, my school adopts this block schedule. Here's what my actual seventh grade schedule looks like under the block:

Odd days: per. 1 Exploratory Wheel (Art/Shop), per. 3 P.E., per. 5 Core English

Even days: per. 2 Success (Study Skills), per. 4 Algebra I, per. 6 Core History

Here "Core" means that all seventh graders have the same teacher for English and History (a way to ease young students into the idea of having multiple teachers). Thus having them for an entire block isn't that much different from the original timeline where I have periods 5-6 each day. Spending extra time in my other classes will be much different from the real timeline.

As far as my friends and fellow students are concerned, I suspect that not much would be different on this timeline as compared to the original timeline. The only difference here is that students in some of my classes (especially Wheel and P.E.) might become slightly more influential, now that I'd see them in longer classes and immediately before a break (snack or lunch). Otherwise, I expect seventh grade under COVID-91 to be mostly like my actual seventh grade year.

What If? COVID-93

Originally, one of the years I selected for a COVID What If? on the old blog was COVID-93. This is because here schools close in March of 1994 (my seventh grade year) and the pandemic extends into my eighth grade year. This corresponds to the grades I covered during the long-term sub assignment last year -- and the whole purpose of this What If? exercise is to empathize with my students.

But now I risk the COVID-91 and COVID-93 What Ifs clashing with each other. My intent was for each What If? to span the length of the real COVID-19 pandemic (since after all, each What If? just transfers the entire pandemic into a different year).

Yet no one knows when exactly "the end of the COVID-19 pandemic" will be. On one hand, the pandemic is clearly still ongoing, with yet another Greek letter variant (omicron) just announced. We might keep having new variants for the next decade, exhausting the Greek alphabet. The pandemic might even become endemic -- that is, it might never go away (just like the flu). On the other hand, if by "the pandemic" we mean the set of restrictions done in the name of the disease, then that could end as soon as today -- many people blame certain politicians (such as Governor Newsom or President Biden) for the restrictions that they believe are unnecessary.

I'm not sure what to say about politics here. But as far as my COVID What Ifs are concerned, the pandemic is still ongoing, since teachers and students are still wearing masks. In the COVID-91 universe, I'm still wearing masks in late 1993 (fall n+2, corresponding to 2021). If the masks extend into spring 1994 (n+3, corresponding to 2022), then it will officially intersect the COVID-93 What If?

While there's no reason to avoid intersecting What Ifs (as each one takes place in its own universe), it's not desirable. There's no reason to write two stories about 1994, one where the pandemic is waning but we're still wearing masks, and another where the pandemic is just starting. If the pandemic does extend into the n+3 year, then I'll probably abolish either the COVID-91 or COVID-93 What Ifs.

Here's what I want to say about the COVID-93 What If now? The schools close in March of my seventh grade, and distance learning takes over most eighth grade. Thus freshman year is the year when I hope that things go back to normal.

But recall what I blogged about my freshman year at the start of this month. In November 1995, I moved from my old 7-12 high school to a new 9-12 high school in another district. This means that under COVID-93, I spend the first three months of 1995 in distance learning (packets), April through June back at school (under a sort of hybrid where I attend only certain days of the week), July and August on summer vacation, September and October fully in-person (five days per week), and then November and December in my new district high school.

Also, under COVID-93, the first part of seventh grade is on the old pre-pandemic schedule, while my freshman year is on the new block schedule. Notice that the school I attend in November and December also had a seven-period block schedule in 1995 (on the original timeline) with tutorial at the end of the day, and so the transition is more straightforward for me. (Well after I graduated from there, my alma mater has since switched to an eight-period day. But that change has nothing to do with the pandemic -- recall that only pandemic-induced changes will make it into the What If? stories.)

Freshman year is also the year that I join the Cross Country team -- but scheduling XC on a block schedule is tricky. In November, my new school scheduled XC for seventh period and replaced fourth period with a special sports tutorial. But I don't know what my 7-12 school, with its new block schedule, does for athletes. If it schedules sports during a single period 1-6, then practice can only be held three times a week (on the days that period meets). But I have no idea whether it has anything like a sports tutorial.

For the sake of this What If? let's assume that my 7-12 school also has a sports tutorial -- we'll even schedule it for fourth period (just like my new 9-12 school). We'll switch my fourth period class (on the original timeline) to sixth period (when sports practice occurred on the original timeline):

Odd days: per. 1 History, per. 3 Science, per. 5 English, Cross Country

Even days: per. 2 French II, per. 4 Sports Tutorial, per. 6 Algebra II, Cross Country

What If? COVID-96 (NEW)

On the old blog, one of the COVID What If? I chose was COVID-97. In this story, the schools close March of my junior year, and the closure extends into my senior year. The first normal year works out to be fall 1999, when I begin studying at UCLA.

But once again, the goal of these stories is for me to relate more to my current students. And right now, I'm teaching mostly high school seniors (with a few juniors) -- not college freshmen. In order for this What If? to line up with most of my students' experience, I must choose COVID-96 instead. Since COVID-96 and COVID-97 obviously intersect, and thus I'm abolishing the COVID-97 What If? story.

Moreover, just as COVID-93 deals with the start of my Cross Country career, the original COVID-97 What If? dealt with the end of my XC career. But that story fell apart -- in that story, enough runners drop XC during the pandemic to get me into the top 9 on the team and hence a Varsity spot. But on the original timeline in 2021, the postseason races (like CIF and the State Meet) were cancelled, and so transferring this to 1999, I'd end up making Varsity for nothing. There were CIF meets in Track, but it's much harder to make Varsity in Track than in XC, and for me to make Varsity Track is unrealistic.

So by making it COVID-96 instead of COVID-97, the schools close in March of my sophomore year (just as it did for my current seniors). Then it's my junior year of XC that ends up in spring of the n+2 year when the CIF races are cancelled, and now I return in fall as a senior with a more realistic hope of making the Varsity team.

In figuring out what a pandemic XC season might look like, I looked at my high school XC website and followed the career of a certain runner -- one whose running times are similar to my own. That runner was a junior last spring -- so under COVID-97, I was (improperly) matching up my senior times with a junior runner. Now under COVID-96, I can match up senior vs. senior, so now a comparison with this runner makes more sense. (But now notice that this runner is a bit faster than I was -- after all, he was running my senior times when he was a junior.)

So what did the XC season look like for this runner (my alter ego, so to speak)? He started with by running in the mid-19's at a trial, then ran sub-13 -- in a two-mile race, not three miles! (Sub-13 for three miles would be close to the world record.) He ran in the mid-18's in the famous Woodbridge Invitational (a race that I ran in the original timeline, and earned a similar time). His time was just under 18 in the first cluster meet of the year, then sub-13 in another two-mile race. (What's with all of these two-mile races? Also, it's interesting that my alter ego can break 18 for three miles, but can barely run sub-13 for two miles.) The next two races were on hilly courses -- just over 20 minutes at the second dual meet, and sub-19 on the famous Mt. SAC course. He capped off the regular season by running 17:54 at League Finals -- this was close to my final time on the original timeline as well.

What does this mean for Varsity and CIF? Well, the CIF results aren't posted on the website, but I notice that his ranking on the team was somewhere in the teens. Since he's nowhere near the top 9, it means that my alter ego doesn't make the Varsity team -- and if he didn't make the Varsity team, would it be right to say that I'd have made it under COVID-96?

This is a tricky one. Notice that while he was ranked #15 or #16, I, running similar times, was ranked a bit higher at #12. There are many more runners in the 16- and 17-minute range now than there was back when I ran. Also, all I need are for three runners ahead of me to drop XC during the pandemic for me to make Varsity -- as far as I know, three runners really did drop from my school team in 2021, yet my alter ego is still stuck in the teens.

Well -- since this is my story, I'm going to say that I somehow make the Varsity team. Let's assume that the top three runners (the ones most heavily invested in XC) stay on the COVID-96 team. Of the next three runners, two are freshmen and one is a senior. I'm not sure who's more likely to drop XC due -- a senior who misses junior year and doesn't come back after the pandemic, or a freshman who was never on XC in the first place. At any rate, the #5 freshmen has an older brother on the team, so he's probably joining the COVID-96 team as well. This means that we can choose to drop any three runners out of the #4-11 range (excluding #5) in order for me to become the #9 runner and advance to CIF Prelims. (OK, I just chose it at random -- the #4, #9, and #11 runners all drop. Two of these are freshmen who end up never joining the team, and #9 is a senior who leaves during the pandemic.)

Notice that in any race, only seven runners can actually run -- #8 and #9 are alternates. On the original timeline, our coach ran the #9 alternate in the CIF Prelims race instead of our #7 -- probably because he was a senior, and the coach wanted to give him the opportunity to run. Since our #9 leaves the team due to COVID-96, I become the senior who gets to run CIF. Since this race is on the Mt. SAC course, I'll give myself a mark of 18:45 in this race (right around the time my alter ego ran at Mt. SAC).

I won't speculate whether this team (missing some of its top runners) can advance beyond CIF Prelims into CIF Finals (or even State) -- I wouldn't get to run in those races as an alternate. All that matters is that on the COVID-96 timeline, I end my career by running at CIF Prelims.

While it will be stressful to attend class as a senior after missing a year due to the pandemic, being able to run XC and make it to Varsity will make it a whole lot easier -- and a lot more fun.

Oh, and by the way, as a senior in high school, I took BC Calculus. Notice that I don't teach BC, since there wouldn't be enough such students at my tiny school. At least one of my Stats students did take AB last year as a junior -- he's now taking Stats, since BC is not an option.

On the other hand, I already posted about the one guy who ran XC at my current school. Recall that I watched him in what turned out to be his final race.

What If? COVID-08

This What If? places the pandemic during my career as a teacher rather than a student. As I wrote on the original blog, here the schools close in March 2009 -- right in the middle of my student teaching. I explained that I end up completing my student teaching in fall 2009. (In the COVID-08 world, this would be distance learning -- perhaps something like Skype.) But now we reach fall 2010 -- that is, the n+2 year -- and now I wonder, what would my career look like here?

Once again, we compare to the original timeline. In the real year 2010, I had trouble landing a teaching job due to the Great Recession, and my career stalls. But in the real year 2021, I obviously do have a teaching position now -- and I suspect that the reason this position was open was the pandemic. And so I suspect that in the COVID-08 world, I will get my first teaching job in 2010 after all.

Where would I be hired in 2010? It wouldn't be at my current 2021 school, since this school didn't even exist in 2010. The most logical answer is that it would be at the same school where I complete my student teaching -- in other words, a position opens when a teacher leaves due to COVID-08. Then my name comes up for the position due to my recency at the school.

Recall that this school was in the Los Angeles Unified School District (LAUSD). As a student teacher, I covered one period of Algebra I and two periods of Algebra II, so it's possible that, if an Algebra I or II position opens up, I'd be placed in that position.

I'm not sure how successful I'd be in this position. A wildcard here is classroom management -- due to the pandemic, I spend all of my student teaching on Skype, but then my first year as a teacher would be back to in-person learning. As you're aware, I definitely would need more practice with management, but I don't get much opportunity on Skype.

Also, I'm not sure how the pandemic would clash with the recession. Back then, all new LAUSD teachers can expect to get pink-slipped every March 15th. So even if I get hired during the COVID-08 pandemic, I might still find myself with a pink slip in March 2011 (the n+3 year).

What If? COVID-14

This last What-If? is similar to COVID-08. The schools close in March 2015, during the first year of my original blog (so you should know from there that I was subbing at the time). Like COVID-08, I'd expect to be hired at a school in fall 2016 during the pandemic -- except that I was hired on the original timeline anyway, at the old charter school. So we might as well let the old charter school be where I'm hired after the pandemic.

I've already mentioned one way that this might be different from the original timeline -- the field trip to the LA County Fair. Due to the pandemic, the fair will now open in May 2022 instead of September -- and so this pandemic-induced change transfers to the COVID-14 timeline.

Another major change is that during the pandemic, I become accustomed to online software (even while I'm subbing). This will help me at the charter school -- I'll be much quicker to use software (especially Study Island and Illinois State Science, since I must also teach science) than on the original timeline, and this will help me be a better teacher. At the very least, I don't have to give everyone an A in science, since now I can establish science grades.

Plans for Ethnostats

The day before yesterday, I wrote extensively about my plans for Calculus, general Stats, and Trig, but not much about my Ethnostats class. Well, here are some ideas.

Earlier in this post, I wrote about my Cross Country career, and what it might have looked like during the COVID-93 or COVID-96 pandemics. Meanwhile, tomorrow will be (unlike last year, but like most normal years) the California State Meet in XC. This means that it will be time for my annual watching of the McFarland USA movie -- one of the (very) few XC movies that I know of. (That's if we don't count tomorrow's airing of the Christmas special Robbie the Reindeer -- it's all about the "Reindeer Games" which is a bit like a XC race or the Olympics.)

And then I was thinking -- why don't I show the McFarland USA movie in my Ethnostats class? After all, it contains themes that are relevant to an Ethnic Studies class. There is a culture clash between the white coach and his Hispanic (mostly Mexican-American) runners. The young athletes must make a choice between competing for the team and providing for their families (mainly by working very hard in the fields). Even the school-to-prison pipeline is mentioned in the movie (indeed, McFarland High School is right across the street from the prison). And of course, the lone XC runner at the school is right in my Ethnostats class.

I'd like to show the film as soon after the actual State Meet as possible. I wouldn't mind showing it on Monday, but that's an all-classes day, so there won't be enough time for the movie. This means that the most likely day to play the movie will during the Wednesday block.

I'll have to come up with some assignment to go with the movie, to make sure that the students are watching it and not playing with their phones the entire period. There might be some notes to write and post on Google Classroom, or maybe something to write on another page in their Stats scrapbook. It's likely that I will do both.

Once again, I will cover Chapter 10 in both general Stats and Ethnostats. This chapter is on samples -- and in Ethnostats, I'll be able to tie the lesson to the surveys they took before Thanksgiving (which, of course, involved taking a sample). There will be Quiz #4 and a final in this class. The second semester will start will Chapter 11.

Cheng Art of Logic in an Illogical World, Chapter 2

Chapter 2 of Eugenia Cheng's The Art of Logic in an Illogical World is called "What logic is." Here's how it begins:

"If I eat chocolate then I am happy. Is that logical?"

Cheng asks several similar questions about what is or isn't logical -- how touching wood makes her feel better, and how it's often cheaper to fly to a suburb of London than the capital itself, even though the plane actually lands in London en route to the suburb. But then Cheng's next example is:

"If you are white, then you have white privilege. Are these things logical?"

Cheng proceeds:

"The innocuous little word 'if' has a whole range of slightly different means. Some of them, but not all of them, encapsulate the most important building block of logical argument -- logical implication."

Again, I'm glad that our side-along reading of Cheng's book lines up with Chapter 2 of the U of Chicago text -- didn't we just read about "if" in Lessons 2-2 and 2-3? Anyway, the author shows us how important logic is to the study of mathematics:

"Logic is to mathematics as evidence is to science."

But Cheng provides us many uses of "if" in English that aren't logical. "If I eat chocolate then I am happy" is a personal taste, not logic. "If you eat your broccoli then you can have ice cream" is a bribe, not logic. "If you walk my dog for me then I'll pay you twenty quid" is an agreement, not logic. "If you are over 75 then you don't have to take your shoes off when going through airport security" is a rule, not logic:

"The difference is a bit blurry in real life, but we can try and find the distinction by thinking about examples."

The author tells us that the above examples are better described as "non-logical" or "alogical" rather than illogical. For examples of logical statements, Cheng returns to the contentious example:

• If you have white privilege then you have privilege.
• If you are white then you have white privilege.
• If you are white in Europe or the US then you have white privilege.
• If you are white in a place that has white privilege then you have white privilege.

Cheng points out that the last statement is logical because it's almost tautological (or pointless). The statements above depend on the definition of "white privilege," which she will discuss in more detail in a later chapter.

"If we continue to use normal everyday language we are doomed to have problems being completely logical because the words we use are not completely logically defined, but we can get close enough that to call it anything other than logical would, in my opinion, be pedantry rather than precision."

Cheng next writes about social services. Here she distinguishes between false negatives -- those who deserve help but don't get it -- and false positives -- those who don't deserve help but do get it:

• If you care more about false negatives than false positives you will believe in expanding social services.
• If you care more about false positives than false negatives you will not believe in expanding social services.

I've thought about this myself (but never blogged about it, since such politics is usually off-topic for this blog), but I could never express myself as elegantly -- or logically -- as Cheng does here. And in fact, she compares social services to jetlag:

• If you're better at staying awake tired than falling asleep not tired you should deprive yourself of sleep in advance of crossing time zones.
• If you're better at falling asleep not tired than staying awake tired you should not deprive yourself of sleep in advance of crossing time zones.

Cheng writes that these two ideas are similar. Staying awake when tired is a false positive, while falling asleep when not tired is a false negative. She writes that she herself is a false positive, so she stays awake before she travels across the pond.

The author proceeds to write about how logic leads to discovery:

"If a statement follows from pure logic then it has to be true, automatically. Saying it out loud doesn't exactly add new information, but it does add new insight."

To illustrate this, Cheng returns to her white privilege example again:

1.  If you are white then you have white privilege.
2. If you have white privilege then you have privilege.

From these two statements we now have the implication "if you are white then you have privilege."

Now Cheng tells the remarkable story of Kyle MacDonald, an internet legend who ultimately traded a paper clip for a house. Here's how he did it:

paper clip -> pen shaped like a fish -> hand-sculpted doorknob -> camping stove -> 1000-watt generator -> "instant party" (beer keg with neon sign) -> snowmobile -> two-person trip to Yakh, British Columbia -> a large van -> a recording contract with Metalworks -> a room for a year in Phoenix, Arizona -> an afternoon with rock star Alice Cooper -> a part in a Corbin Bernsen film -> a house in Kipling, Saskatchewan

Of this story, the author writes:

"But I am really fascinated by this mental version of an optical illusion, where you can take tiny steps that don't seem too surprising, and get somewhere that is extremely surprising and a very long way from where you started. This is how logic works."

And of course, we do this all the time in Geometry classes -- we call it a "proof." Cheng writes about another example -- in his book The Power of Habit, Charles Duhigg argues that requiring a higher level of science achievement in teachers would eventually reduce birth defects in babies:

"It is an example of a masterful construction of a long chain of implications in normal life."

Now Cheng introduces the formal notation for implications. We've seen this notation a few days ago in Lesson 2-2 of the U of Chicago text -- "A => B" means "If A then B" or "A implies B." (Even though the notation appears in Lesson 2-2, I don't use it on a worksheet until tonight's lesson.)

She tells us that a proof is basically a whole series of implications strung together like this:

A => B
B => C
C => D

We can then conclude that A => D. Here are some longer chains of implications given by Cheng:

1. If you say women are inferior, that is insulting to women.
2. If you think that "feminine" is an insulting way to describe a man, you are saying that women are inferior.
3. Therefore if you think that "feminine" is an insulting way to describe a man, you are insulting women.

Here is another:

1. If you don't stand up for minorities being harassed then you are letting bigotry flourish.
2. If you let bigotry flourish you are complicit with bigotry.
3. If you are complicit with something bad then you are almost as bad as it.
4. Therefore if you don't stand up for minorities being harassed you are almost as bad as a bigot.

Cheng points out that whether A is true for a particular person has no effect on whether the entire implication A => B is true:

"'If you are a US citizen or permanent resident you are required to have health insurance' is true whether or not you are in fact a citizen or resident. The implication doesn't tell us whether or not someone needs health insurance; we only know they do if we already know they are a citizen or resident."

The author tells us that there are several things we must check before we attempt to start a proof:

1. We should carefully define the concepts we're talking about.
2. We should carefully state the assumptions we're making.
3. We should carefully state exactly what we're going to prove, in an unambiguous way.

Here Cheng writes about something I've mentioned a few times on the blog -- the gender pay gap:

"For example, in arguments about why women earn less than men, on average, sometimes people assume that women don't care about earning money as much as men do."

But, as the author goes on to point out, she doesn't accept the implication that if women don't care about making money then they should be paid less for the same job. Cheng puts it succinctly and flatly: "I think that is exploitation."

Cheng warns us that arguments might break down due to problems of knowledge:

• Unstated assumptions, or using stated assumptions incorrectly.
• Incorrect definitions, or incorrect use of definitions.

Here is an example from the book: "...in arguments about clinical depression when people assume that depression is caused by circumstances and therefore there is no reason a successful person should be depressed."

Proofs also break down due to problems of logic:

• Gaps in the logic; leaping from one statement to another without justifying it, or leaving out too many steps in between.
• Incorrect inferences: this is when a logical step is made that is actually incorrect, where you say something follows from something else, but it doesn't.
• Handwaving: arriving at a conclusion without true use of logic, but by metaphorically waving your hands around enough that people think you are.
• Incorrect logic: there are many subtle ways that incorrect logic can get slipped into arguments as logical fallacies....

"An example of an incorrect inference is the view that 'scientists agree with each other, which shows there is a conspiracy.'"

Cheng repeats a story first told by Stephen Hawking -- an audience member insists that the world is standing on the back of a turtle, and in fact, "it's turtles all the way down." But we must be sure that our proofs start somewhere rather than stand on an infinite stack of turtles:

"Where does all this originate from? As I have mentioned, I think the process of working backwards is just like small children who ask 'Why?' repeatedly."

There are some questions that logic can't answer, like "Do I exist?" or "What is the meaning of life?":

"To be a moderately functioning adult, we have to stop asking those questions at some point -- not necessarily permanently, but at least for some part of every day."

And so in logic we must start with some basic assumptions -- which the author calls "axioms" -- with which everyone agrees beforehand. Another word for "axiom" is "postulate" -- and that's the word that appears in most Geometry texts, including Lesson 1-7 of the U of Chicago text.

Cheng concludes with a preview of the next chapter:

"The logic must all flow out of that starting point. In the next chapter we'll talk about the direction of that flow. Like time, logic has a direction and we must not try to violate it."

Conclusion

This concludes the second of my two Thanksgiving break posts. I'll resume with my normal school year blogging pattern on Monday.